The premise behind McKeown's work and all his books is very powerful stuff. Many people don't breathe properly (through the mouth, not using the diaphragm, etc.), which leads to a state of permanent hyperventilation (taking in too much oxygen). Contrary to popular belief, too much oxygen is not a good thing. It causes all kinds of health problems: anxiety, poor digestion, sleep apnea, insomnia, the list goes on.
In Atomic Focus, McKeown is emphasizing the relationship between poor breathing and poor concentration, in particular an overly busy and cluttered mind. Unfortunately, it doesn't hit the mark. It really would have benefited from a good editor. Frankly, it is poorly written and poorly structured. It feels like a grab bag of loosely tied together ideas. There are so many books out there about time management and focus that deal with these topics much better. McKeown should have stuck with what makes his approach unique - breathing.
Also, if you're looking for the science to back up this theory (hyperventilation = poor health), I would look elsewhere. Possibly one of McKeown's other books goes deeper into that territory. Or check out the writing of Buteyko, whose work provides the basis for McKeown's. Still, the breathing exercises are good, and I imagine the same across all his books. And if you're serious about improving your breathing in order to experience all kinds of health benefits, then the exercises are what matter.